Helical gearsets

ABSTRACT

A new design for helical gearsets is disclosed in which the new gearsets meet all applicable ratings and standards of the American Gear Manufacturers Association (AGMA), and yet allows very substantial cost savings over prior similar gearsets having an equivalent AGMA rating. The gearsets of the instant invention generally are substantially thinner, and have fewer, but larger, gear teeth than the prior gearsets they replace. A helical gearset of the present invention includes a pinion and a gear, with the pinion and the gear having a plurality of teeth. Each of these teeth has a helix angle ranging between about 18 degrees and 33 degrees. The pinion and the gear each have a face width and a whole depth, with the pinion having 13 or fewer teeth, and with the pinion and the gear having a face width-to-whole depth ratio of about 4.5 or less. The axial overlap of the gearset ranges between 1.001 and about 1.2.

BACKGROUND OF THE INVENTION

This invention relates to gearsets, and more particularly, to helicalgearsets. More specifically, the gearsets disclosed herein are singlehelical gearsets utilizing steel gear blanks, in which the gear teethare hobbed or otherwise formed and then are carburized (or otherwisehardened) and ground (if necessary) to an acceptable American GearManufacturers Association (AGMA) quality and reliability level, and inwhich the gearsets are AGMA rated.

Generally, a gearset comprises a pinion in mesh with a gear, the smallerbeing the pinion and the larger being the gear. Depending on whether thepinion or the gear is the driven member, the gearset may be a speedreducer or a speed increaser. In this disclosure, the term "speedreducer" will be utilized. However, within the broader aspects of thisinvention, it will be recognized that the gearsets of the presentinvention may be utilized with speed increasers as well as with speedreducers.

The gear ratio is the number of teeth on the gear divided by the numberof teeth on the pinion. Helical gears have teeth which spiral around thebody of the gear, and the helix angle is the inclination of the geartooth in lengthwise direction with respect to the axis of rotation ofthe pinion or the gear. Helical gearsets generally have two or moreteeth in contact with one another at any given time (referred to asoverlap), and the contact begins at one end of the tooth and extendsalong a diagonal line across the width of the tooth. Generally, helicalgears are favored over spur gears because they can carry higher loads athigher speeds, and are generally of smoother and quieter operation.However, it will be understood that spur gears are merely one embodimentof helical gears in which the helix angle is 0 degrees. Thus, thegearsets of the present invention apply to spur gears as well as tohelical gears.

Gear designs have been an evolving art over many centuries. As moreinformation has become known about mathematics, gear geometry,kinematics, strength of material, fabrication, and lubrication, much ofthe complicated gear design information and operational knowledge hasbeen condensed into more manageable formulas or "rules of thumb", whichallow the gear designer to design and manufacture gearsets havingdesired operational characteristics and load-carrying capabilities. Overthe years, the American Gear Manufacturers Association (AGMA), ofArlington, Va., has developed and published a series of standards andratings which enable gear designers and users to make ratingcalculations to establish that a given gearset is suitable in size andquality to meet the specified requirements of a gear application (i.e.,to ensure that the gearset will transmit a specified horsepower at aknown speed under a desired loading condition for a predeterminedservice life). These AGMA standards and ratings are updatedperiodically, and thus are an accurate reflection of the current stateof the art in gear design and manufacture. In many gear applications,there is a contractual obligation that the gearing must meet allapplicable AGMA standards.

In the design of helical involute gear teeth, AGMA standards requirethat the gear tooth design have sufficient bending strength and pittingresistance to result in a gearset which will carry its intendedhorsepower load for a prescribed service life with a desired level ofreliability. Generally, the bending strength of gear teeth is afatigue-related phenomena, dependent on the resistance to cracking ofthe gear tooth at the tooth root fillet caused by repeated applicationof bending loads to each tooth each time the gear tooth is in mesh withits mating gear. Pitting resistance is also a fatigue-relatedphenomenon. However, pitting is a result of contact pressures (i.e.,Hertz stresses) between the meshing gear teeth of the gearset exceedingthe limitations of the gear tooth material. In rating a gearset, it isnecessary to rate the gearset both with regard to its resistance topitting at a rated load (typically expressed in horsepower), and withregard to bending strength at its rated load or horsepower. The lower ofthe pitting resistance power rating or the bending strength power ratingis then used as the power rating for that gearset. AGMA Standard 218.01,dated December, 1982, sets forth the pitting resistance and bendingstrength of spur and helical involute gear teeth. AGMA Standard 218.01is herein incorporated by reference.

Over the years prior to this invention, gearset designs have evolvedwhich work well for their intended uses or applications. As advances inknowledge came along, the AGMA standards were updated so that the AGMAstandards reflected both the state of the art and operational experienceof many gear manufacturers or users of gears made in accordance withAGMA standards. However, in general, the AGMA standards or ratings didnot take the cost of manufacturing a gearset into account. Instead, aseries of general design guidelines or rules of thumb of helical geardesign evolved. First, it was generally recognized that the ratio ofpinion face width divided by pinion pitch diameter should be 1.5 orless, so as to avoid torsional twist of the pinion which tends toconcentrate the load on one end of the pinion. Additionally, except forextremely low speed (e.g., about 50 rpm or less) applications, theminimum number of pinion teeth should be 14 or more. However, for mostapplications, 16 or more pinion teeth are preferred. A fewer number ofteeth will result in unsatisfactory wear and undue noise. In helicalgearsets, the face overlap (overlap) should be 1.2 or greater so as toensure that, at all times, there is load sharing by adjacent teeth.Additionally, it is usually advisable to keep the helix angle relativelylow (e.g., 5-15 degrees) so as to limit the thrust loads applied to thehelical gear.

As noted above, cost considerations are not taken into account by theAGMA standards and rating system, and are not reflected by theabove-noted generally followed design guidelines. However, geardesigners have developed some costing rules of thumb which are usuallytaken into account during the design of a gearset. Generally, it washeretofore thought that a helical gearset having the shortest centerdistances and the widest faces practical are most cost-effective. Also,coarse pitches were thought to be more costly than fine pitches. As willbe noted, these cost guidelines are at direct odds with the above-noteddesign guidelines in many respects.

Over the years, helical gearset designs have evolved which work well andmeet the AGMA standards and rating system. However, the questionremained: Were the prior art gearsets the most economical designs whichmet the AGMA rating standards?

SUMMARY OF THE INVENTION

Among the several objects and features of this invention may be notedthe provision of gearsets which meet AGMA ratings and standards, and yetwhich reflect a very significant cost savings (e.g., 20-35 percent) overolder similar designs of the same rating capacity;

The provision of such gearsets which are of significantly lighter weightthan the prior equivalent gearsets which they replace;

The provision of such gearsets which may be much more readily fabricatedwith existing gear production machines than the prior gearsets whichthey replace;

The provision of such gearsets which are of compact design, thusrequiring less shaft space within a speed reducer or the like; and

The provision of a gear design methodology which allows gearsets havingthe above-noted features to be designed.

Other objects and features of this invention will be in part apparentand in part pointed out hereinafter.

Briefly stated, a helical gearset of the present invention comprises apinion and a gear, with the pinion having a having a normal operationalrotation speed up to about 2400 rpm or more. The pinion and gear eachhave a plurality of teeth. Each tooth has a helix angle ranging betweenabout 18 degrees and 33 degrees. The pinion and the gear each have aface width (i.e., active face width) and a whole depth (i.e., the radialdepth of the tooth from the addendum circle to the dedendum circle). Thepinion has 13 or fewer teeth, and the pinion and the gear each have aface width-to-whole depth ratio of about 4.5 or less.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a side elevational view of a pinion in mesh with a gearconstituting a gearset having a gear-tooth ratio (i.e., the number ofteeth on the gear divided by the number of teeth on its mating pinion)of five;

FIG. 2 is a perspective side elevational view of a portion of a helicalpinion made in accordance with this invention, illustrating standardhelical gear terminology;

FIG. 3 is a flat pattern layout of the gear teeth of the helical gearpinion shown in FIG. 2, and further illustrating helical gearterminology;

FIG. 4 is a view similar to FIG. 3 of a typical gear of the presentinvention (shown in solid lines) compared with an equivalent prior artgear (shown in phantom) having the same AGMA rating;

FIGS. 5 and 6 illustrate, in block diagram form a first step in theselection of a gearset of the present invention in which the geometry ofthe gearset is evaluated to determine if the geometry is acceptable;

FIG. 7 illustrates, in block diagram form, how the geometry of thegearset is varied if the geometry as determined in FIGS. 5 and 6, is notacceptable;

FIG. 8 illustrates the methodology of finding the cost of a gearset, asselected by the methodology of FIGS. 5-7;

FIG. 9 is a more detailed illustration of the costing methodology ofFIG. 8;

FIG. 10 is a vertical cross sectional view of a shaft mount speedreducer, utilizing the gearsets of the present invention; and

FIG. 11 (sheet 1) is a view similar to FIG. 2, comparing a pinion of thepresent invention to an equivalent prior art pinion having the same AGMArating and having the same pitch circle, this drawing figureillustrating that the pinion of the present invention has substantiallyfewer teeth and that the face width of the pinion of the presentinvention is substantially narrower than the face width of the prior artpinion.

Corresponding reference characters indicate corresponding partsthroughout the several views of the drawings.

DESCRIPTION OF PREFERRED EMBODIMENTS

Referring now to the drawings, and particularly to FIG. 1, a gearset, asindicated in its entirety at 1, is shown to comprise a gear 3 mountedfor rotation on its center C_(G). A pinion 5 is in mesh with gear 3, andthe pinion is mounted for rotation on its center C_(P). As illustrated,the gearset 1 has a gear-tooth ratio (i.e., the number of teeth on thegear divided by the number of teeth on its mating pinion) of five.However, within the broader aspects of this invention, any gear-toothratio may be utilized.

More specifically, gear 3 and pinion 5 are shown to be helical gears,each having a plurality of helical gear teeth 7 formed thereon in meshwith one another, as shown in FIG. 1. As shown in FIG. 2, in which onlya segment of pinion 5 is illustrated, conventional helical gearterminology is listed. FIG. 3 is a flat pattern layout of a segment ofpinion 5, and additional helical gear terminology is listed thereon.

In order to develop the design of a helical gearset of the presentinvention, which meets the American Gear Manufacturers Association(AGMA) standards and ratings, and which, in accordance with thisinvention, reflects very significant cost savings (e.g., ranging betweenabout 20-35 percent over prior art gearset designs having the equivalentAGMA ratings), a methodology of design was utilized which not only rateda wide variety of gearset parameters to ensure that the gearsets were inconformance with AGMA standards and ratings, but fabrication costs weretaken into account as well. In this methodology, as will be hereinafterset forth in detail, as few as possible of the gearset design parameterswere fixed, and the old gear design guidelines heretofore discussed andthe previous cost guidelines were not taken into account.

Generally, in the methodology utilized to develop the gearsets of thepresent invention, the gearset ratio, the gear center distances, thepower to be transmitted, and the input or output speed (rpm) were given.As ground rules utilized in the methodology of the present invention,the gearsets were to be helical gears and were to be fabricated fromsteel blanks, preferably, but not necessarily, from forged steel blanks.The gearsets were to be carburized and ground. However, other heattreating methods may be used. Also, predetermined quality andreliability levels were established. From geometry considerations, itwas decided that the pinion would have 11 or more teeth. Since helicalgearsets were to be utilized, it was necessary to have a face overlapgreater than one so that the rating procedure of helical gears could beused.

In FIGS. 5-9, a complete block diagram flow chart of the methodology ofthe present invention, utilized to design or choose gearsets of thepresent invention, is shown.

As shown in FIGS. 5 and 6, a first step in the selection of a gearsetfor a given horsepower, speed (rpm), ratio, and center distance wasevaluated to determine that the geometry of the gearset would result ina proper gearset having acceptable geometry. As shown in FIG. 7, if thegeometry is not acceptable or proper, the tooth combination wasadjusted, holding to the number of pinion teeth constant and maintainingan acceptable ratio, was repeatedly carried out until such time as thegeometry of the gearset was acceptable. Once an acceptable geometry wasfound, the acceptable gearset was then rated in accordance with AGMArating standards 218.01, December, 1982, which is herein incorporated byreference.

More particularly, in accordance with AGMA rating standard 218.01, thegearset was rated both with regard to pitting resistance strength, andwith regard to bending strength power (see FIG. 6). The lower ratingpower (i.e., either the lower of the pitting resistance power rating, orthe bending strength power rating) was utilized. If the horsepowerrating was not acceptable (i.e., if the gearset would not carry thespecified horsepower as determined by the initial input), then the facewidth of the gearset was adjusted until an acceptable horsepower ratingwas found.

Then, as shown on FIGS. 7 and 8, the cost of manufacturing the gearsethaving an acceptable horsepower rating was determined. Generally, thesecosts included the cost of the material (i.e., the gear blanks) fromwhich the gearset was made, the hobbing costs, and the grinding costs.More specifically, the costing subroutine is illustrated in detail inFIG. 9.

This procedure resulted in gear information generally similar to thatshown in Table 1 below. More specifically, the gear information setforth in Table 1 is for a 6.250 inch center distance gearset, having aratio of 5.00. In Table 2, additional information is presented for thegearset described in Table 1 at various operating speeds. The gearsetsdescribed in detail in Tables 1 and 2 are for gearsets N-207-5-HS andN-207-LS, as listed on Table 3 hereafter presented.

                  TABLE 1                                                         ______________________________________                                        Gearset Information                                                           N-207-5-HS and N-207-LS                                                       ______________________________________                                                       6.250 - 8         Ratio 5.0000                                                Pinion            Gear                                         ______________________________________                                        Number of teeth                                                                              13                65                                           Normal Diametral Pitch  7.00000                                               Normal Pressure Angle   20.00000                                              Helix Angle             26.45238                                              Operating Center Distance                                                                             6.25000                                               Face Width              1.06400  (F/D = 0.491)                                Outside Diameters                                                                            2.4519            10.6195                                      Base Circle Diameter                                                                         1.9216             9.6080                                      Standard Pitch Diameter                                                                      2.0743            10.3716                                      Operating Pitch Diameter                                                                     2.0833            10.4167                                      Normal Operating; Pressure Angle 20.53914; Helix                              Angle 26.55164 Base Helix Angle 24.74556; Transverse Diametral                Pitch 6.26713 Transverse Pressure Angle; STandard 22.12332;                   Operating 22.72577 Contact Ratio; Total 2.36676; Transverse                   1.31069; Face 1.05607                                                         Stress Correction Factor                                                                     1.4798        1.5958                                           Tooth Form Factor                                                                            0.4951        0.5304                                           Min. Length of Contact 1.51625 AGMA Load Sharing Ratio                        0.70173                                                                       0.00021-0.00020                                                                         J-Factor    0.4768          0.4736                                            I-Factor             0.25013                                                  K-Factor =  1625                                                              Unit Load = 19743                                                   ______________________________________                                    

                  TABLE 2                                                         ______________________________________                                        Gearsets N-207-5-HS and N-207-LS                                              6.250-8                                                                                        Pinion   Gear                                                       Pitting   Bending  Bending                                                                              Pitch                                               Resistance                                                                              Strength Strength                                                                             Line                                         Gear   Rating    Rating   Rating Velocity                                                                             Speed                                 Speed  (HP)      (HP)     (HP)   (FPM)  Pinion                                RPM(G) PAC       PAT(P)   PAT(G) PLV    RPM(P)                                ______________________________________                                        10.00  2.627     2.479    2.462  27.    50.00                                 20.00  5.204     4.910    4.877  55.    100.00                                30.00  7.750     7.312    7.264  82.    150.00                                40.00  10.272    9.692    9.628  109.   200.00                                50.00  12.774    12.053   11.973 136.   250.00                                60.00  15.259    14.397   14.301 164.   300.00                                70.00  17.727    16.726   16.615 191.   350.00                                80.00  20.182    19.042   18.915 218.   400.00                                90.00  22.623    21.345   21.203 246.   450.00                                100.00 25.052    23.637   23.480 273.   500.00                                110.00 27.470    25.918   25.746 300.   550.00                                120.00 29.877    28.189   28.002 327.   600.00                                130.00 32.274    30.451   30.248 355.   650.00                                140.00 34.661    32.703   32.486 382.   700.00                                150.00 37.040    34.947   34.715 409.   750.00                                160.00 39.409    37.183   36.936 437.   800.00                                170.00 41.771    39.411   39.149 464.   850.00                                180.00 44.124    41.632   41.355 491.   900.00                                190.00 46.470    43.845   43.553 519.   950.00                                200.00 48.808    46.051   45.745 546.   1000.00                               210.00 51.140    48.251   47.930 573.   1050.00                               220.00 53.464    50.444   50.108 600.   1100.00                               230.00 55.782    52.631   52.281 628.   1150.00                               240.00 58.093    54.812   54.447 655.   1200.00                               250.00 60.398    56.986   56.607 682.   1250.00                               260.00 62.697    59.155   58.762 710.   1300.00                               270.00 64.990    61.319   60.911 737.   1350.00                               280.00 67.277    63.477   63.055 764.   1400.00                               290.00 69.559    65.630   65.193 791.   1450.00                               300.00 71.835    67.777   67.326 891.   1500.00                               310.00 74.106    69.920   69.455 846.   1550.00                               320.00 76.372    72.058   71.578 873.   1600.00                               330.00 78.632    74.191   73.697 901.   1650.00                               340.00 80.888    76.319   75.811 928.   1700.00                               350.00 83.139    78.442   77.920 955    1750.00                               360.00 85.385    80.561   80.025 982.   1800.00                               370.00 87.626    82.676   82.126 1010.  1850.00                               380.00 89.863    84.787   84.222 1037.  1900.00                               390.00 92.095    86.893   86.314 1064.  1950.00                               400.00 94.323    88.995   88.402 1092.  2000.00                               410.00 96.546    91.093   90.486 1119.  2050.00                               420.00 98.766    93.187   92.566 1146.  2100.00                               430.00 100.981   95.277   94.643 1174.  2150.00                               440.00 103.192   97.363   96.715 1201.  2200.00                               450.00 105.399   99.445   98.783 1228.  2250.00                               460.00 107.602   101.524  100.848                                                                              1255.  2300.00                               470.00 109.801   103.599  102.910                                                                              1283.  2350.00                               480.00 111.997   105.670  104.967                                                                              1310   2400.00                               490.00 114.189   107.738  107.021                                                                              1337.  2450.00                               500.00 116.377   109.803  109.072                                                                              1365.  2500.00                               ______________________________________                                         Cost of Gearset: Total $81.08, including material costs of $17.26, hobbin     costs of $27.31, and grinding costs of $36.51, using 1984 costing data.  

More specifically, Table 2 sets out additional information of theexemplary gearset shown in Table 1 throughout a range of speeds. Thefirst column of Table 2 gives the speed of the gear (rpm (G)). Thesecond column, as indicated by PAC, is the pitting resistance of thegearset expressed in horsepower. The third column, as indicated by PAT(P), indicates the bending strength of the pinion, expressed inhorsepower. Likewise, the fourth column indicates the bending strengthof the gear, also expressed in horsepower. The fifth column, indicatedby PLV, indicates the pitch line velocity of the gearset, expressed infeet per minute. Lastly, the seventh column indicates the rotationalspeed of the pinion, as expressed in rpm.

Further referring to Table 2, the cost of the new gearsets, identifiedas N-207-5HS and N-207-LS, is calculated, using 1984 cost data from theassignee of this invention, the Browning Manufacturing Division, EmersonElectric Co., Maysville, Ky., was found to be $81.08. Of this amount,$36.51 can be allocated to grinding costs, $17.26 is allocated tomaterial costs, and $27.31 can be allocated to hobbing costs. Ascomparison, the actual cost of the equivalent rated old gearset,O-207-5-HS (as shown in Table 3), which the new gearset replaces isabout $117.61, representing 31.1 percent savings.

It will be undersood that the gearset costs disclosed herein are costindexes and not the total costs of manufacturing the gearsets. Thesecost indexes only reflect some of the more important cost parameters,such as material costs, hobbing costs, and grinding costs. Other costs,such as machining bores, keyways, bar cutoff, etc. are not taken intoaccount.

The methodology shown in FIGS. 5-8 is in accordance with this inventionused to obtain proper AGMA rated gearsets. This was done by assigningthe pinion 11 teeth, or by sizing the gearset so as to have 55 totalteeth, whichever is greater. This defined the minimum pitch and thegearset tooth combination. This minimum pitch was then incrementallyincreased one pitch at a time until it was incremented by 6 to 9pitches, depending on ratio. At each pitch increment, gear toothcombinations were found. Then, the amount of overlap of each particulargearset was incrementally varied in predetermined steps (i.e., overlapwas varied from 1.001 to 2.0 in step sizes of 0.1).

To hold the overlap, the helix angle must likewise be held. Thoseskilled in the art will recognize that there is a physical relationshipbetween face, pitch, helix angle, and overlap. To do this, the centerdistance was made "nonstandard" by enlarging and contracting (i.e.,decreasing or increasing) the number of teeth on the "standard" centerdistance.

Each resulting gearset was evaluated to ensure that it was ageometrically proper gearset. Each of these resulting gearsets was alsorated in accordance with the AGMA rating standards, and it was costed inaccordance with the methodology here above described and shown in FIG.9. The aforementioned process was repeated for a multiplicity ofgearsets by repetitive pitch increases, whereupon the least costlygearset meeting both rating and geometry constraints was selected.

In accordance with this invention, the above-noted methodology wasapplied to a series of gearsets utilized in whole product line of shaftmount speed reducers, as indicated generally at 9 in FIG. 10. Morespecifically, shaft mount speed reducer 9 includes a split housing 11with the housing halves sealably joined together by bolts 13. The speedreducer has an input shaft 15. A gear train, as generally indicated at17, is mounted within the housing. This gear train includes a first orhigh speed gearset 19, and a second or low speed gearset 21. Moreparticularly, the high speed gearset 19 includes a high speed pinion 23integral with the input shaft 15. The high speed pinion 23 is in meshwith a high speed gear 25. The high speed gear 25 is a compound gearhaving a low speed pinion 27 associated therewith. Thus, compound gear,including high speed gear 25 and low speed pinion 27, is mounted on anintegral shaft 29 and journaled within suitable bearings 31 relative tothe housing. The low speed pinion 27 is in mesh with a low speed gear33. The latter is mounted on a quill 35, which in turn is journaled inbearings 37 carried by the housing. The quill includes a tapered bushing39, as is described in detail in the co-assigned U.S. Pat. No. 4,626,114which constitutes the output shaft of the speed reducer, and whichprovides for the easy mounting and off-mounting of the speed reducerrelative to its application. For further details of the construction ofa speed reducer utilizing the gearsets of the present invention,reference may be made to the coassigned U.S. Pat. No. 4,626,114 which isherein incorporated by reference.

As is conventional, a series of speed reducers is provided by mostmanufacturers to accommodate a variety of applications, ranging frominput horsepowers from one quarter horsepower up to 200 horsepower, instandard sizes 107 through 608 (i.e., standard output bore sizes rangingbetween 1 and 7/16 inches through 6 and 1/2 inches). Additionally, theconventional ratios for these gear reducers include 5 to 1, 9 to 1, 15to 1, and 25 to 1.

It will be understood in certain speed reducers, the low speed gearset(e.g., pinion 23 and gear 25) may be utilized as the high speed gearsetof a higher rated speed reducer.

Referring now to Table 3, a comparison of the gearsets of a previousline of shaft mount speed reducers, such as is shown in FIG. 10, isshown compared to the new gearsets of the present invention, which theyreplace. The gearset identification is shown, for example, to includethe designation "O-107-5-HS" and "N-107-5-LS". In these gearsetidentifications, the "O" denotes the old or prior art design, and the"N" designation designates the new gearset design of the presentinvention. The designation "107" designates the unit size. Thedesignation "5" designates the overall ratio of the speed reducer inwhich this gearset is used. It will be noted that if the gearsetidentification number does not include a number similar to thislast-mentioned number, that the gearset is common to all ratios in thisunit size. Lastly, the designations "HS" and "LS" mean high speed (orinput gearset member) and low speed (or output gearset member),respectively. For the gearsets of Table 3 which cost comparisons areshown, both the old and new gearsets have essentially the same AGMArating.

                                      TABLE 3                                     __________________________________________________________________________    Comparison of Old and New                                                     Gearsets of Equivalent AGMA Ratings                                                                         6                                                       1        3            Face                                            Gearset Nom.                                                                              2    Active                                                                             4   5   Width/   8                                      Identi- Dia.                                                                              Helix                                                                              Face Pinion                                                                            Gear                                                                              Whole                                                                             7    Cost                                   fication                                                                              Pitch                                                                             Angle                                                                              Width                                                                              Teeth                                                                             Teeth                                                                             Depth                                                                             Overlap                                                                            $                                      __________________________________________________________________________    O-107-5-HS                                                                            16  26°11'04"                                                                   .930 17  86  6.33                                                                              2.107                                                                              63.2                                   N-107-5-HS                                                                            11  32°8'18"                                                                    .635 12  61  2.97                                                                              1.183                                                                              46.3                                   O-107-9-HS                                                                            16  26°11'04"                                                                   .562 32  46  3.83                                                                              1.264                                       N-207-9-HS                                                                            20  19°29'54"                                                                   .475 32  58  4.04                                                                              1.009                                       O-207-15-HS                                                                           16  26°11'04"                                                                   .562 23  55  4.04                                                                              1.264                                       N-107-15-HS                                                                           18  27°41'45"                                                                   .390 20  55  3.83                                                                              1.039                                       O-107-25-HS                                                                           16  26°11'04"                                                                   .562 16  63  3.83                                                                              1.264                                       N-107-25-HS                                                                           18  31°10'27"                                                                   .383 12  61  2.93                                                                              1.136                                       O-107-LS                                                                              16  26°11'04"                                                                   .930 14  86  6.38                                                                              2.107                                       N-207-LS                                                                              11  32°8'18"                                                                    .635 12  61  2.97                                                                              1.183                                       O-115-5-HS                                                                            12  22°28'51"                                                                   1.0625                                                                             16  82  5.43                                                                              1.552                                                                              70.3                                   N-115-5-HS                                                                            9   27°34'0"                                                                    .765 12  60  2.93                                                                              1.014                                                                              53.0                                   O-115-9-HS                                                                            12  35°57'36"                                                                   .6875                                                                              28  39  3.51                                                                              1.542                                       N-115-9-HS                                                                            14  25°10'44"                                                                   .541 23  42  3.22                                                                              1.026                                       O-115-15-HS                                                                           16  26°11'04"                                                                   0.6875                                                                             29  67  4.68                                                                              1.545                                       N-115-15-HS                                                                           13  31°59'45"                                                                   .468 15  41  2.59                                                                              1.026                                       O-115-25-HS                                                                           16  26°11'04"                                                                   0.6875                                                                             19  77  4.68                                                                              1.545                                       N-115-25-HS                                                                           15  26°56'26"                                                                   .511 11  56  3.26                                                                              1.105                                       O-115-LS                                                                              12  22°28'51"                                                                   1.0625                                                                             13  82  5.42                                                                              1.552                                       N-115-LS                                                                              9   27°34'0"                                                                    .765 12  60  2.93                                                                              1.014                                       O-203-5-HS                                                                            10  22°14'0"                                                                    1.250                                                                              16  81  5.32                                                                              1.506                                       N-203-5-HS                                                                            7.5 31°6'41"                                                                    .893 11  56  2.85                                                                              1.102                                       O-203-9-HS                                                                            12  33°57'35"                                                                   0.750                                                                              33  46  3.83                                                                              1.600                                       N-203-9-HS                                                                            11  32°0'0"                                                                     0.540                                                                              22  41  2.53                                                                              1.002                                       O-203-15-HS                                                                           12  33°57'35"                                                                   0.750                                                                              23  55  3.83                                                                              1.600                                       N-203-15-HS                                                                           11  31°0'0"                                                                     0.560                                                                              17  47  2.62                                                                              1.010                                       O-203-25-HS                                                                           16  26°11'01"                                                                   0.750                                                                              23  91  5.11                                                                              1.685                                       N-203-25-HS                                                                           12  27°15'57"                                                                   0.580                                                                              12  60  2.96                                                                              1.015                                       O-203-LS                                                                              10  22°14'0"                                                                    1.250                                                                              13  81  5.32                                                                              1.506                                       N-203-LS                                                                              7.5 31°6'41"                                                                    0.893                                                                              11  56  2.85                                                                              1.102                                       O-207-5-HS                                                                            10  22°14'0"                                                                    1.6875                                                                             18  91  7.18                                                                              2.032                                                                              117.61                                 N-207-5-HS*                                                                           7   26°27'8"                                                                    1.064                                                                              13  65  3.17                                                                              1.056                                                                              81.08                                  O-207-9-HS                                                                            10  33°33'23"                                                                   0.8125                                                                             31  44  3.46                                                                              1.429                                       N-207-9-HS                                                                            12  20°25'59"                                                                   0.762                                                                              31  57  3.89                                                                              1.016                                       O-207-15-HS                                                                           10  33°33'23"                                                                   0.8125                                                                             22  53  3.46                                                                              1.429                                       N-207-15-HS                                                                           11  27°33'47"                                                                   0.6300                                                                             20  55  2.95                                                                              1.021                                       O-207-25-HS                                                                           16  26°11'04"                                                                   0.8125                                                                             25  103 5.53                                                                              1.826                                       N-207-25-HS                                                                           11  32°8'18"                                                                    0.6350                                                                             12  61  2.97                                                                              1.183                                       O-207-LS                                                                              10  22°14'0"                                                                    1.6875                                                                             15  91  7.18                                                                              2.032                                       N-207-LS*                                                                             7   26°27'8"                                                                    1.064                                                                              13  65  3.17                                                                              1.056                                       O-215-5-HS                                                                            8   21°17'14"                                                                   1.9375                                                                             18  88  6 60                                                                              1.791                                       N-215-5-HS                                                                            5.5 32°26'14"                                                                   1.178                                                                              11  56  2.76                                                                              1.106                                       O-215-9-HS                                                                            10  33°33'23"                                                                   1.000                                                                              38  52  4.26                                                                              1.759                                       N-215-9-HS                                                                            10  18°56'11"                                                                   0.973                                                                              30  55  4.14                                                                              1.005                                       O-215-15-HS                                                                           10  33°33'23"                                                                   1.000                                                                              27  64  4.25                                                                              1.759                                       N-215-15-HS                                                                           9   28°11'25"                                                                   0.840                                                                              19  52  3.22                                                                              1.137                                       O-215-25-HS                                                                           12  33°57'35"                                                                   1.000                                                                              22  87  5.11                                                                              2.134                                       N-215-25-HS                                                                           0   27°34'0"                                                                    0.765                                                                              12  60  2.93                                                                              1.014                                       O-215-LS                                                                              8   21°17'14"                                                                   1.9375                                                                             14  88  6.60                                                                              1.791                                       N-215-LS                                                                              5.5 32°26'14"                                                                   1.178                                                                              11  56  2.76                                                                              1.106                                       O-307-5-HS                                                                            8   21°17'14"                                                                   2.625                                                                              19  94  8.94                                                                              2.427                                       N-307-5-HS                                                                            5   26°44'41"                                                                   1.404                                                                              12  61  2.99                                                                              1.006                                       O-307-9-HS                                                                            10  33°33'23"                                                                   1.0625                                                                             40  54  4.52                                                                              1.869                                       N-307-9-HS                                                                            7.5 25°14'48"                                                                   1.005                                                                              25  46  3.21                                                                              1.023                                       O-307-15-HS                                                                           10  33°33'23"                                                                   1.0625                                                                             28  66  4.52                                                                              1.869                                       N-307-15-HS                                                                           7.5 28°45'43"                                                                   .914 18  50  2.92                                                                              1.050                                       O-307-25-HS                                                                           10  33°33'23"                                                                   1.0625                                                                             19  75  4.52                                                                              1.869                                       N-307-25-HS                                                                           7.5 31°6'41"                                                                    0.893                                                                              11  56  2.85                                                                              1.102                                       O-307-LS                                                                              8   21°17'14"                                                                   2.625                                                                              15  94  8.94                                                                              2.427                                       N-307-LS                                                                              5   26°44'41"                                                                   1.404                                                                              12  61  4.42                                                                              1.006                                       O-315-5-HS                                                                            6   21°0'44"                                                                    3.25 15  71  8.30                                                                              2.226                                                                              244.90                                 N-315-5-HS                                                                            5   17°59'14"                                                                   2.078                                                                              13  68  4.42                                                                              1.021                                                                              189.99                                 O-315-9-HS                                                                            10  33°33'23"                                                                   1.250                                                                              37  54  5.32                                                                              2.199                                       N-315-9-HS                                                                            7   23°1'48"                                                                    1.237                                                                              28  51  3.68                                                                              1.078                                       O-315-15-HS                                                                           10  33°33'23"                                                                   1.25 26  64  5.32                                                                              2.199                                       N-315-15-HS                                                                           6.5 28°29'8"                                                                    1.087                                                                              19  52  3.01                                                                              1.073                                       O-315-25-HS                                                                           10  33°33'23"                                                                   1.25 17  74  5.32                                                                              2.199                                       N-315-25-HS                                                                           7   26°27'8"                                                                    1.064                                                                              13  65  3.17                                                                              1.056                                       O-315-LS                                                                              6   21°0'44"                                                                    3.25 12  71  8.30                                                                              2.226                                       N-315-LS                                                                              5   17°59'41"                                                                   2.078                                                                              13  66  4.42                                                                              1.021                                       O-407-15-HS                                                                           10  33°33'23"                                                                   1.500                                                                              34  87  6.38                                                                              2.639                                       N-407-15-HS                                                                           6.5 28°29'8"                                                                    1.087                                                                              19  52  3.01                                                                              1.073                                       O-407-25-HS                                                                           10  33°33'23"                                                                   1.500                                                                              23  98  6.38                                                                              2.639                                       N-407-25-HS                                                                           7   26°27'8"                                                                    1.064                                                                              13  65  3.17                                                                              1.056                                       O-407-LS                                                                              6   21°0'43"                                                                    3.1875                                                                             15  88  8.14                                                                              2.183                                       N-407-LS                                                                              3.75                                                                              25°14'56"                                                                   1.984                                                                              11  55  2.32                                                                              1.010                                       O-415-15-HS                                                                           8   21°17'14"                                                                   1.500                                                                              31  82  5.11                                                                              1.387                                       N-415-15-HS                                                                           6   28°0'0"                                                                     1.400                                                                              20  55  3.57                                                                              1.255                                       O-415-25-HS                                                                           8   21°17'14"                                                                   1.500                                                                              21  93  5.11                                                                              1.387                                       N-415-25-HS                                                                           6   31°0'0"                                                                     1.350                                                                              12  61  3.45                                                                              1.328                                       O-415-LS                                                                              5   21°34'0"                                                                    3.8125                                                                             14  79  8.11                                                                              2.230                                       N-415-LS                                                                              3.75                                                                              25°0'0"                                                                     2.830                                                                              12  61  4.52                                                                              1.428                                       O-507-15-HS                                                                           8   21°17'14"                                                                   1.8125                                                                             34  83  6.17                                                                              1.676                                       N-507-15-HS                                                                           5   29°44'24"                                                                   1.520                                                                              19  52  3.23                                                                              1.200                                       O-507-25-HS                                                                           8   21°17'14"                                                                   1.8125                                                                             23  94  6.17                                                                              1.676                                       N-507-25-HS                                                                           5.5 29°14'21"                                                                   1.568                                                                              13  66  3.67                                                                              1.341                                       O-507-LS                                                                              5   21°34'0"                                                                    4.125                                                                              16  97  8.78                                                                              2.413                                       N-507-LS                                                                              3.75                                                                              14°48'0"                                                                    3.365                                                                              15  75  5.37                                                                              1.026                                       O-608-15-HS+                                                                          6   22°20'48"                                                                   2.500                                                                              30  78  6.38                                                                              1.815                                       N-608-15-HS                                                                           5   25°13'6"                                                                    2.334                                                                              20  55  4.97                                                                              1.583                                       O-608-25-HS+                                                                          6   22°20'48"                                                                   2.500                                                                              20  87  6.38                                                                              1.815                                       N-608-25-HS                                                                           5.5 22°15'50"                                                                   2.479                                                                              14  71  5.80                                                                              1.644                                       O-608-LS+                                                                             4   14°25'47"                                                                   5.500                                                                              16  94  9.36                                                                              1.724                                       N-608-LS                                                                              3.75                                                                              11°18'0"                                                                    4.865                                                                              17  86  7.76                                                                              1.138                                       __________________________________________________________________________     *Described in detail in Tables 1 and 2.                                       +608 old style has 22.5 pressure angle gearing; all other gearing is          20° pressure angle.                                               

Referring to Table 3, columns 1-8 list several characteristics of theold and new gearsets used in the above-noted line of shaft mount speedreducers. It is believed that columns 1-5 indicate characteristics whichwill be well known to those skilled in the art and do not requirediscussion. However, with regard to column 6, the ratio of face width towhole depth, this characteristic of both the prior art gearsets and thegearsets of the present invention is a good dimensional indication ofthe non-obvious characteristics of the gearsets of the presentinvention, compared to equivalently rated prior art gearsets. Generallyspeaking, as illustrated in FIGS. 4 and 11, pinions and gears ofgearsets of the present invention are substantially narrower thanequivalently rated prior art gearsets and, the gears and pinions of thepresent invention have significantly fewer, but bigger, teeth thanequivalently rated gearsets of the prior art gearsets wherein the gearsand pinions of both the present invention and the prior art gearsetshave substantially identical pitch diameters (see FIG. 11). Theface-to-whole depth ratio is a meaningful indication of the narrowerface widths and larger teeth of the gearsets of the present invention.

Column 7 of Table 3 compares the overlap of the old and new gearsets.Generally, the new gearsets of the present invention have asubstantially lower overlap than the prior, equivalently rated gearsetswhich they replace. It is observed, from Table 3, that the new gearsetsof the present invention have overlaps as near to 1.000 (or slightlygreater) as possible. In comparison, many of the old gearsets hadoverlaps in excess of 1.500, with certain of the prior gearsets havingoverlaps greater than 2.000.

In accordance with this invention, the overlap for smaller size gearsetsshould be greater than 1.000 but less than about 1.25 and preferablyless than about 1.100. For larger sizes of gearsets of the presentinvention, it is preferably that the gearsets have an overlap as smallas possible ranging between 1.001 and about 1.6.

Further referring to Table 3, column 3, it will be noticed that insubstantially all cases, the active face width of the new gearsets isless, and in most cases substantially less, than the face width of theprior art similarly sized in AGMA rated gears which they replace. It isto be understood that all of the new gearsets 1 shown in Table 3 areAGMA rated and are manufactured to AGMA Quality 10 tolerances like theold gearsets they replace. Both the old and the new gearsets were formedfrom forged steel blanks, and the gear teeth were carburized and groundafter the gear teeth had been formed. However, within the broaderaspects of this invention, steel gears of other blanks, formingtechniques, heat treatment, and finishing may be made.

Referring to the number of pinion teeth (column 4, of Table 3), it willbe noted that in almost all cases, the pinions of the gearsets 1 of thepresent invention (i.e., the new gearsets) have substantially fewerteeth than the pinions of their equivalent old gearsets. As washeretofore noted, as a prior art general design guideline, it wasgenerally advisable for a gearset to have 14 or more (preferably 16 ormore) pinion teeth so as to provide a gearset of smooth operation, andso as to avoid undue wear of the pinion teeth. Surprisingly, it has beenfound that the new gearsets, with substantially fewer teeth (well belowthe heretofore recommended minimum number of teeth), and with the activeface widths of the new gear sets being, in most cases, substantiallyless than the active face widths of the old gearsets which they replace,result in new gearsets which have equivalent AGMA ratings, which havereliabilities at least as great as (and in most cases greater than), theold, equivalent gearsets, and which result in quiet, smooth operation ofthe gearsets and the speed reducers in which they are utilized.

It should also be noted that, as a general rule (but not in all cases),the helix angle (column 2 of Table 3) of the new gearsets of the presentinvention are oftentimes equal to or somewhat larger than the helixangle of the old equivalently rated gearsets which they replace.According to prior art design guidelines, the helix angle should be aslow as possible (e.g., 5-15 degrees). Upon reviewing the gearset datapresented in Table 3, it will be noted, that generally (but not in allcases), the gearsets 1 of the present invention have helix anglesranging between about 18 degrees and 33 degrees. Further, the pinion 5and the gear 3 of each gearset 1 of the present invention generally hasa face width to whole depth ratio of about 4.5 or less. Also, a majorityof the gearsets 1 of the present invention have 13 or fewer pinionteeth.

As noted above, the general characteristics of the gearsets of thepresent invention are not universally followed within all of thegearsets shown in Table 3. However, it will be remembered that in regardto the gearset selection methodology, as set forth in FIGS. 5-9, thecost of the gearset was a driving factor of the gearsets actuallyselected. More specifically, in regard to FIG. 9, it will be noted thattwo determinations were the cost of hobbing the gear and the cost ofgrinding the gear after carburizing. These costs are directly related tothe machines on which the hobbing and grinding operations are carriedout. In certain instances, it was more economical to have gearsetswherein the pinions had more than 13 pinion teeth, and wherein theface-to-whole depth ratio was greater than 4.5, because these gearsetscould be more economically fabricated on the hobbing and grindingequipment presently available. However, if the constraints of fitting aparticular gearset size to existing hobbing and grinding equipment werenot present, it is believed that many of the gearsets shown in Table 3which have more than 13 pinion teeth, and which have a face width/wholedepth ratio greater than about 4.5, would not be utilized. As shown inFIG. 2, the whole depth is the whole depth of the gear teeth or the sumof the addendum and the dedendum. Also, those skilled in the art willrecognize that hobbing tools (i.e., the metal cutting elements of ahobbing machine) and that grinding tools or wheels are onlyconventionally available in discrete pitch sizes.

In other words, if available machine and tool limitations and gear casedesign constraints in calculating gearing costs were not required to betaken into account in the design of the gearsets shown in Table 3, it isbelieved that with most, if not all, of the new gearsets would have 13or fewer teeth, and would have a face-to-whole depth ratio of 4.5 orless. Even more preferably, it would be found that the face-to-wholedepth ratio of the new gearsets would be about 3.25 or less.

As previously noted, the gearsets of the present invention, as indicatedby the new gearsets in Table 3, are substantially less costly than theirequivalent AGMA rated gearsets, as indicated by the old gearsets inTable 3, which they replace in a series of shaft mount speed reducers.In general, the cost savings realized by replacing the old gearsets ofthe shaft mount speed reducer line shown in Table 3 with the newgearsets also shown in Table 3, have resulted in cost savings for thegearsets, on the average of about 20-35 percent. In Table 3, costcomparisons of four old and new gearsets are shown. These costcomparisons illustrate typical cost savings in accordance with thisinvention. It will be understood that both the old and the new gearsetshave the same gear ratio and essentially the same AGMA rating.Additionally, both the old and the new gearsets were formed from forgedsteel blanks, and were carburized and ground.

Within the broader aspects of the present invention, those skilled inthe art will recognize that the gearsets hereinabove discussed relate tohobbed, carburized, and ground steel gearsets. However, those skilled inthe art will recognize that the methodology and gearset characteristicsherein described in regard to the gearsets of the present invention maybe utilized to determine gearsets for other applications which do notutilized hobbed, carburized and ground gears. For example, both themethodology and the gearset information herein disclosed and claimed maybe utilized for steel, induction hardened, or through hardened gearsetsas well. Also, gear blanks other than forged steel blanks may be used.

In view of the above, it will be seen that the other objects of thisinvention are achieved and other advantageous results obtained.

As various changes could be made in the above constructions or methodwithout departing from the scope of the invention, it is intended thatall matter contained in the above description or shown in theaccompanying drawing shall be interpreted as illustrative and not in alimiting sense.

What is claimed is:
 1. A helical gearset comprising a pinion and a gear wherein the pinion has a normal operational rotation speed of up to 2400 rpm or greater, said pinion and said gear each having a plurality of teeth, each said tooth having a helix angle ranging between about 18 degrees and 33 degrees, said pinion and said gear each having a face width and a whole depth, said pinion having 13 or fewer teeth, and said pinion and said gear each having a face width to whole depth ratio of 4.5 or less.
 2. A helical gearset as set forth in claim 1 wherein said pinion and said gear are carburized and ground.
 3. A helical gearset as set forth in claim 1 wherein face width to whole depth ratio is preferably about 3.25 or less.
 4. A helical gearset as set forth in claim 1 wherein said helix angle of said pinion and said gear ranges between about 21 degrees and 30 degrees.
 5. A helical gearset comprising a pinion and a gear wherein the pinion has a normal operational rotation speed of up to 2400 rpm or greater, said pinion and said gear each having a plurality of teeth, said pinion and said gear each having a face width and a whole depth, said pinion having 13 or fewer teeth, and said pinion and said gear each having a face width to whole depth ratio of 4.5 or less.
 6. A helical gearset comprising a pinion and a gear wherein the pinion have a normal operational speed of up to 2400 rpm or greater, said pinion and gear each having a plurality of teeth, each said tooth having a helix angle ranging between 18 degrees and 33 degrees, said pinion and said gear each having a face width and a whole depth, said pinion having 13 or fewer teeth, said pinion and said gear having a face width to whole depth ratio of 4.5 or less, and said gearset having an axial overlap ranging between 1.001 and 1.2.
 7. A gearset as set forth in claim 6 wherein said overlap ranges between 1.001 and about 1.1. 